A multidimensional stochastic precipitation model with major emphasis on its spectral structure is proposed. As a hyperbolic type of stochastic partial differential equation, this model is characterized by a small set of easily estimable parameters. These characteristics are similar to those of the noise-forced diffusive precipitation model, but the representation of the physical and statistical features of the precipitation field is similar to that of the Waymire-Gupta-Rodriguez-Iturbe (WGR) precipitation model. The derivation was based on the autoregressive process considering advection and diffusion, the dominant statistical and physical characteristics of the precipitation field propagation. The model spectrum showed a good match with the Global Atlantic Tropical Experiment spectrum. This model was also compared with the WGR model and the noise-forced diffusive precipitation model both analytically and through applications such as the sampling error estimation from spaceborne sensors and rain gauges. The sampling error from spaceborne sensors based on the proposed model was similar to that of the noise-forced diffusive precipitation model, but much smaller than that of the WGR model. Similar results were also obtained in the estimation of the sampling error from rain gauges. ¿ American Geophysical Union 1996